I have tried dozens of IQ tests and literally hundreds of 'IQ-like' puzzles. I have also studied the concept thoroughly. Therefore, what do IQ tests really measure? Mainly, they are simple tests of deductive reasoning, inductive reasoning and general knowledge across a number of domains. What then is missing?
From the tests I have taken, the following are usually missing:
Short-term memory: you have just studied a chapter of calculus. Do you: 1) have to look back at the chapter to remember the formulae, or 2) is that information stored in memory and at your fingertips? If 2) is true, you have an advantage over the people who answered 'yes' to 1). Yet this is missing from most tests.
Concentration: when you work at a task: do you laser-in on the task and focus for hours or does your attention drift? If you can laser-in, you have a big advantage intellectually over those who cannot.
Working memory: child prodigies at mathematics, chess, and music often have high levels of this. When you are doing a math problem, can you hold seven bits of information in your mind at once or eleven? The more information you can hold in your mind, the better you can solve the problem. A professional mathematician or chess player could probably think dozens of 'moves' ahead. However, this is sometimes missing from IQ tests.
Creativity: Can you look at a problem in new and unexpected ways? Can you generate dozens of ideas? Again, this is often missing.
Anyway, like I said, IQ tests are just generally tests of inductive reasoning, deductive reasoning, and general knowledge. Do not look at them as fatally flawed but as imperfect. Nonetheless, there is much empirical support for the professional ones that are developed and normed properly. Please keep all of this in mind...